If you are "aware" you might know that 99% of nuclear waste is low-level (contaminated hospital waste, rags, paper) or intermediate-level (cladding, concrete or chemicals from decommissioned reactors that are irradiated). These will never go critical. Even high-level radioactive waste doesn't go critical because the hot parts are either (a) valuable and get reprocessed into new fuel or (b) have short half lives and decay within a few month in the spent fuel pool of the power plants before being shipped away.
There's 47 k tones of high level waste in the US alone [1].So I think it's fair to assume that your 80 000 tonnes world wide was high level waste.
Which has to be kept far apart from each other since they decay and at the very least generate heat. Therefore, apartness is an integral part of repository design. Yucca Mountain has a capacity for 70 000 tonnes. That is, its not big enough to store the world's waste despite nuclear power having a small fraction of the overall worldwide power production over the last 60 years.
[1] https://en.wikipedia.org/wiki/High-level_radioactive_waste_m...
But never-mind the technicalities, you cannot dismiss the geo-political implications. We have barely existed as a species in the time length nuclear waste decays. We have only 5000 years or so of statehood, the vast majority of them since collapsed.
Unless you propose burying the waste in the Marianna trench (I think there is merit there), I really need to see the stability concerns addressed.
EDIT: And yes, I am "aware". I stated my undergrad in a nuclear eng program, and switched to physics after a few courses. I still have friends in the industry and to say morale is low is an understatement.